) and log of distance (
). The angle and distance are measured in relation
to the centre of the image, .backlinks: /SRSoftwareOverview
The log-polar transform warps an image onto new axes, angle () and log of distance (). The angle and distance are measured in relation
to the centre of the image, .
Using the centre of the image as the axis reference, pixel coordinates are given by
the angle is
and, with a base of 
, the log of the distance is
The base, chosen so the diameter of the transformed image is the same as that of the input image, is
where 
is the minimum dimension (probably
height) of the input image.
When warping images, it is often impractical to use the forward transform. Since we use discrete coordinates (i.e. integer x and y values), more than one input coordinate may map to the same output coordinate. Even worse, not every output coordinate will be covered.
One solution is to calculate the irregular grid of coordinates obtained by transforming each input coordinate (without discretising). Then, the grid is resampled (using interpolation) at the required output positions.
An easier (and sometimes less computationally intensive) method is to reverse the process. For each output coordinate, the transformation is applied in reverse, to obtain a coordinate in (or outside) the input image. Using interpolation, a value is determined.
This can be done if, neglecting the effect of discretisation, the transformation function is bijective (one-to-one correspondence, and all input and output coordinates are mapped).
Given and , we
would now like to find 
and 
. First, we calculate the distance 
from the centre:
whereafter we can determine and as
rainbow
